Testing the homogeneity of the Universe using gamma-ray bursts

In this paper, we study the homogeneity of the GRB distribution using a subsample of the Greiner GRB catalogue, which contains 314 objects with redshift $0<z<2.5$ (244 of them discovered by the Swift GRB Mission). We try to reconcile the dilemma between the new observations and the current theory of structure formation and growth. To test the results against the possible biases in redshift determination and the incompleteness of the Greiner sample, we also apply our analysis to the 244 GRBs discovered by Swift and the subsample presented by the Swift Gamma-Ray Burst Host Galaxy Legacy Survey (SHOALS). The real space two-point correlation function (2PCF) of GRBs, $\xi(r),$ is calculated using a Landy-Szalay estimator. We perform a standard least-$\chi^2$ fit to the measured 2PCFs of GRBs. We use the best-fit 2PCF to deduce a recently defined homogeneity scale. The homogeneity scale, $R_H$, is defined as the comoving radius of the sphere inside which the number of GRBs $N(<r)$ is proportional to $r^3$ within $1\%$, or equivalently above which the correlation dimension of the sample $D_2$ is within $1\%$ of $D_2=3$. For the Swift subsample of 244 GRBs, the correlation length and slope are $r_0= 387.51 \pm 132.75~h^{-1}$Mpc and $\gamma = 1.57\pm 0.65$ (at $1\sigma$ confidence level). The corresponding scale for a homogeneous distribution of GRBs is $r\geq 7,700~h^{-1}$Mpc. The results help to alleviate the tension between the new discovery of the excess clustering of GRBs and the cosmological principle of large-scale homogeneity. It implies that very massive structures in the relatively local Universe do not necessarily violate the cosmological principle and could conceivably be present.Comment: 7 pages, 5 figures, accepted by Astronomy & Astrophysics. The data used in this work (e.g. Tables 1 and 2) are publicly available online in electronic form at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A

The creative industrial park : formation path and evolution mechanism

This paper has built a three-stage assumption of creative industrial park on the base of evolutionary economics, which are the gather of units, the construction of interface and the development of network. The gather of units is a reflection of resource search, the construction of interface is a need of identity, and the development of network is a result of multi-dimensional expansion.In the three-stage evolution, the creative industrial park increases constantly their evolution level from the simple geographic gathered to the division and cooperation of labor, until the formation of novel systems. Then this paper analyzes the 798 creative industrial park using the three-stage assumption. This paper finds the main problem of 798’s self-destructing after the low level development of the third stage is the exclusion of the commercial prosperity to the art production. Accordingly,the paper puts forword four modes of promoting the integration between art and commerce. At last, this paper argues the different characteristics of the creative industrial park from other industrial parks. On the angle of formation path, the essence of creative industries is integration of culture and economy, technology. On the angle of evolution mechanism, it reflects novel characteristic of unit, identity characteristic of interface, and co-creation characteristic of network.creative industrial park; formation path; evolution mechanism; integration of culture,economy,and technology

Finslerian MOND versus the Strong Gravitational Lensing of the Early-type Galaxies

The gravitational lensing of Bullet Clusters and early-type galaxies pose serious challenges on the validity of MOND. Recently, Finslerian MOND, a generalization of MOND in the framework of Finsler gravity, has been proposed to explain the mass discrepancy problem of Bullet Cluster 1E 0657\ 558. In this paper, we check the validity of the Finslerian MOND in describing the strong gravitational lensing of early-type galaxies. The investigation on ten strong lenses of the CASTLES samples shows that there is no strong evidence for the existence of dark matter.Comment: 11 pages, 2 figures, 2 table